Mesh quilting for geometric texture synthesis
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Mesh Quilting For Geometric Texture Synthesis. Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일. Abstract. Mesh quilting Geometric texture synthesis algorithm 3D texture sample given in the form of a triangle inside a thin shell around an arbitrary surface

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Mesh Quilting For Geometric Texture Synthesis

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Mesh quilting for geometric texture synthesis

Mesh Quilting For Geometric Texture Synthesis

Kun Zhou et al.

In SIGGRAPH 2006

발표 이성호

2009년 4월 15일


Abstract

Abstract

  • Mesh quilting

    • Geometric texture synthesis algorithm

    • 3D texture sample given in the form of a triangle

      • inside a thin shell around an arbitrary surface

  • Allow interactive and versatile editing and animation

  • Based on stitching together 3D geometry elements

  • On curved surfaces

    • Reduce distortion of geometry elements

      • inside the 3D space of the thin shell

    • Low-distortion parameterization


Introduction

Introduction

  • Today’s commodity video cards

    • Exquisite details can be purely geometrically modeled

  • Modeling such complex geometric details

    • A tedious process

  • Creating mesh-based 3D geometric textures

    • Remains challenging


Mesh quilting

Mesh quilting

  • To synthesize geometric details by stitching together small patches

    • of an input geometric texture sample

  • Tools to further edit and animate

    • these geometric details


Related work

Related work

  • Modeling of Geometric Detail on Surfaces

    • Fur

      • [Kajiya and Kay 1989]

        • Rendering fur with three dimensional textures.

        • In Proceedings of SIGGRAPH 89

    • Volume textures

      • [Neyret 1998]


Mesh quilting for geometric texture synthesis

  • More versatile representations

    • Geometric textures

      • [Elber2005]

    • Shell map

      • [Porumbescu et al. 2005]


Mesh quilting for geometric texture synthesis

  • Limitations

    • Periodic textures

  • Mesh-based creation

    • Of geometric textures on arbitrary meshes

    • [Fleischer et al. 1995]

    • Mostly restricted to the dissemination

      • Of simple texture elements over the surface


Example based texture synthesis

Example-based Texture Synthesis

  • Synthesis based on per-pixel non-parametric sampling

    • [Turk 2001;Wei and Levoy 2001; Ying et al. 2001; Tong et al. 2002; Zelinka and Garland 2003]

  • Based on the L2-norm

    • a relatively poor measure

      • of perceptual similarity,

    • such algorithms are not applicable

      • to a large spectrum of textures.


Mesh quilting for geometric texture synthesis

  • Textures by directly copying small parts

    • of an input texture sample

    • alpha-blending [Praun et al. 2000]

    • quilting

      • [Efros and Freeman 2001; Liang et al. 2001; Soler et al. 2002; Magda and riegman 2003; Kwatra et al. 2003; Wu and Yu 2004; Zhou et al. 2005]

  • Searching for the “min-cut” seams

    • further enhance the smoothness across the seams

      • [Efros and Freeman 2001; Kwatra et al. 2003; Zhou et al. 2005]


Mesh quilting for geometric texture synthesis

  • Feature matching

    • [Wu and Yu 2004]

    • Human visual system is so sensitive

      • to edges, corners and other high-level features in textures

  • Parallel controllable texture synthesis on GPU

    • [Lefebvre and Hoppe 2005]

  • Texture synthesis using Expectation Maximization optimization

    • [Kwatraet al. 2005]


Graphcut textures

Graphcut textures


Shell map

Shell map


Challenges

Challenges

  • Little work to provide tool

    • for 3D geometric texture synthesis.

      • [Bhat et al. 2004; Lagae et al. 2005]

[Lagae et al. 2005]


Mesh quilting for geometric texture synthesis

  • [Bhat et al. 2004]

    • voxel-based approach

  • [Lagae et al. 2005]

    • used distance fields

[Bhat et al. 2004]


Challenges1

Challenges

  • Irregular mesh

    • The input texture sample

      • is not a regular array of pixel values

  • Geometry elements

    • Each being truly a small 3D object identified

      • As a connected component in 3D

  • Quilting is performed on curved surfaces

    • Severe distortion in the 3D space


Contributions

Contributions

  • Mesh-based geometric texture synthesis

    • Synthesized over the base mesh.

  • Triangle meshes

    • Both the input geometry and output geometry

  • Integrity

    • Maintains the integrity of geometry elements

      • In the synthesized texture

      • Texture editing and texture animation

        • can be easily performed


Mesh quilting for geometric texture synthesis

  • Aligns elements

    • through local deformation

    • And merges elements to connect texture patches

  • Mesh quilting on curved surfaces

    • Low-distortion parameterization

      • of the shell space


Mesh quilting synthesis

Mesh Quilting Synthesis

  • Setup & Nomenclature


Algorithm overview

Algorithm Overview

  • Seed Finding

    • Find a seed region R from which to grow the output mesh texture further out

  • Geometry Matching

    • Find the best patch placement around region R using geometry matching to minimize mismatch between the new and the old patch

  • Element Correspondences

    • Find correspondences between elements in the new patch and those in the old patch

  • Element Deformation

    • Align the corresponding elements through local deformation

  • Element Merging

    • Expand the output texture by merging the new patch into the output texture space


Seed finding

Seed Finding

  • Grid-based approach

    • The bounding boxes of both Moutand Min are subdivided in finer regular grids

  • These grids are only two-dimensional

  • Initially, the cells of Moutare tagged unprocessed

  • Each time we wish to grow out the current mesh Mout,

    • we look for an unprocessed cell with the largest number of adjacent cells that are already processed

      • this will be the seed cell that we will try to process next.


Geometry matching

Geometry Matching

  • Find how to complete the mesh texture in the seed cell

    • and possibly add to its surroundings too. Using the nearby existing mesh texture available near the seed cell

    • Find a portion of the original swatch Min best matching this surrounding to extend Mout .


Mesh quilting for geometric texture synthesis

  • Restrict the translation t to be in

    • grid unit

  • Element deformation described in Section 2.6

    • will compensate for an imperfect element alignment

  • Octreedata structure for the input texture

    • Significant speed-up


Element correspondences

Element Correspondences

  • the overlapping region is usually larger than the small sub-patch Pout

    • since the input mesh texture covers Poutcompletely.


Element deformation

Element Deformation


Element merging

Element Merging

  • Every element (either from Cout or Cin) without correspondence

    • directly added to Mout .

  • For every established correspondence (Cout ,Cin)

    • If Cout is entirely within the overlapping region, Cout is ignored

      • and Cinis instead added to the final results

    • if Cin is entirely within the overlapping region,

      • Cinis ignored and Cout is added to Mout .


In all other cases

In all other cases

  • stitch parts of Cin and Cout

    • to get a singly-connected, combined element

    • seek a cut path in each element

    • the graph cut algorithm

      • [Boykov et al. 2001]


Mesh quilting over curved surfaces

Mesh Quilting Over Curved Surfaces

  • Setup

    • Let Mbase be the base mesh that we wish to enhance with added geometric details.

    • Minthe geometric texture mesh

      • used as a swatch

        • seamlessly tile the base mesh

    • S

      • the scale of the geometric details


From planar to curved

From Planar to Curved

  • 2D grid -> base mesh

    • Quilting process will stop

      • Only when there are no more unprocessed triangles

  • Define a local surface patch

    • By starting from the chosen triangle

    • Growing the region

      • Using breadth-first traversal

        • Until we reach a certain depth

        • Or when the total area of the patch exceeds a user-defined threshold


Mesh quilting for geometric texture synthesis

  • Position of vertices located with respect to the base mesh

  • Location of a vertex v

    • over a triangle Tbase

    • is defined by the barycentric coordinates

    • of its orthogonal projection

      • on Tbase

        • along with the orthogonal distance (i.e., height)

          • from the triangle to v


Discrete conformal mapping

discrete conformal mapping

  • surface patch is flattened over the 2D plane

    • using a discrete conformal mapping

      • DCM [Desbrun et al. 2002]


Mesh quilting for geometric texture synthesis

  • Local operations

    • Described for planar mesh quilting

    • Can be performed

      • Over this parameterization plane

  • Position of the newly synthesized vertices

    • Will be reprojected

      • Onto the local mesh-based coordinate system


In very curved regions

in very curved regions

  • If the area distortion induced

    • by the local parameterization is too large

    • Reduce the area of the surface patch

      • This will decrease

        • the size of the output-sub-patch Pout


Final mesh embedding

Final Mesh Embedding

  • Convert the vertex positions

    • Stored in local coordinates for now

    • Into a stand-alone, common embedding

  • Self-intersections can be created

  • Build a texture atlas for Mbase

    • Convert the above local representation of vertex positions to locations

      • in a geometry texture space

  • Then, construct a shell space around Mbase

    • Mapping the vertices

      • from the geometry texture space to the shell space

        • will fix the location of the vertices in 3D space


Shell mapping

Shell Mapping

  • Porumbescu et al. [2005]

    • Creates large distortion in curved regions

  • We alleviate this!

    • By optimizing a stretch metric on this tetrahedral mesh

    • A natural extension of

      • low-distortion parameterization

        • of triangle meshes

      • [Sander et al. 2001]


Minimization algorithm

Minimization Algorithm

  • Only update the u and v texture coordinates of the vertices on the offset surface

  • Optimization of the stretch metric

    • along a randomly chosen search direction

    • in the (u, v) plane

    • as in [Sander et al. 2001].


Discussions

Discussions

  • Regions with very high curvature can be badly handled

    • parametric distortion of small surface patches may be high

  • Cannot always achieve perfect matching

    • if the swatch is untileable

      • even with major element deformation

    • Postprocessing step is performed

      • to remove those visually-displeasingelements

      • Figure 5(b)


Conclusions

Conclusions

  • Mesh-based 3D texture synthesis algorithm


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